VLSN search algorithms for partitioning problems using matching neighbourhoods

Abstract

In this paper, we propose a general paradigm to design very large-scale neighbourhood search algorithms for generic partitioning-type problems. We identify neighbourhoods of exponential size, called matching neighbourhoods, comprised of the union of a class of exponential neighbourhoods. It is shown that these individual components of the matching neighbourhood can be searched in polynomial time, whereas searching the matching neighbourhood is NP-hard. Matching neighbourhood subsumes a well-known class of exponential neighbourhoods called cyclic-exchange neighbourhoods. Our VLSN algorithm is implemented for two special cases of the partitioning problem; the covering assignment problem and the single source transportation problem. Encouraging experimental results are also reported.

Keywords:

• integer programming
• combinatorial analysis
• VLSN search
• partitioning problems
• generalized assignment
• local search

Acknowledgements

This work was partially supported by the NSERC discovery grants awarded to Santosh N Kabadi, KPK Nair, and Abraham P Punnen.